Proportional divider triangle



SePtflo, 1940- H. A. D v. ARlzPE v 2,214,408

PROPORTIONAT.: DIVIDER TRIANGLE Filed Dec. 19, 1936 Stimmen PatentedSept. 10, 1940 A UNITED STATES 'PATENT orrlcs .3; y PROPORTIONALDIVIDIER TRIANGLE.

Harmodio A. de Valle Arizpe, Colonia. Portales,

Mexico, D. F., Mexico i v, .y Application December 19, 1936, serialNo.`116,828 i e: i. zolaims. (cia3-104) y t Y This invention relates toimprovements'in in- Ahole 'lis made through the triangle at thestruments of precision, and its objects are as vertex of the angularlyrelated lines 5, 5. This Ufollow: hole and all similar vholes throughthe triangle,

.11; First, to. provide an instrument for use by is tapered (Fig. 2)from the inscribed face towardw 5 Y students, draftsmen, and the like,which is so the bottom of the triangle.A This formation read- "5 Vconstructed and arranged as to enable the Workily admits the sharppoint'of Yar pencil and at the ing out and delineation of certainmathematical same time confines the point to a very small area @andgeometrical problems involving applied geon the paper underneath. Theoperator has only .n ometry, and this with speed and accuracy; to insertthe point of the pencil When themark,

Second, to provide a simple and accurate deon the paper will appear aslittle more than adot. "10 vice for the purpose stated above, in whichall This dot becomes a reference mark, as presently yof the scalesemployed are uniform, resulting in appears.

again in accuracy over any such device in which A similar tapered hole8j is formed in the trithe scales are non-uniform. anglel at theintersection of the base line -5 with 15 I Other objects and advantageswill appear from a lineS in continuation of the side2 into the re- "1'5the following description, reference being made gion of a. horn Ill atthe right terminal of the to -the accompanying drawing, in which:triangle. The hypotenuse'line 6 stands at a 45 Figure 1 is a plan viewof the improved triinclination toan index jline, II, which is' desangle;'ignated 90 line.` This line lis perpendicular to Figure 2 is a.detailed cross section taken on the baseline 5, and it is used for thepurpose of 2'0 the line 2-2 of Fig. 1; establishing the perpendicularityof any given Figure 3 is a detail cross section taken on the line withrespect to the-base line 5. l'line 3-3 of Fig. 1; The face `of thetriangle is inscribed with a Figure 4 is a diagrammatic Viewillustrating number of scales; These occur inrv two general theuse ofthe triangle in dividing a given line divisions,l one being marked offin a manner sim- 25 i, into a number of equal parts; ilar to .thespacing of a ruler, the other Iconsist- 4 Figure 5 is a diagrammaticview illustrating ing of spaced and numbered holes. It'is confl'the useof the triangle in inscribing a regular templated that inpracticeholesother than those polygon in a given circle; t shown willbelormed in the'triangle at critically Figure 6 is a diagrammatic viewof the triangle and accuratelyllocated places in order to enable 30illustrating its .use in mapping. the solution of mathematical problemsother than This invention lwillbe best understood from a those hereinexplained. *Thescales -in the first ,consideration of the followingdetailed descripdivision are designated I2, I3 and I4. The scale y.".tion in view of the accompanying drawing, but I 2 is regularlydivided `either inl inches and '"35 it is to be understood that theinvention is not fractions thereof-gior, preferably, in centimeters 35"confined to the disclosure, being susceptible of and millimeters. Thescale I2'has l'eft and right such changes and modifications which shallde- .hand origins at the holes 1, 8, as shown'by the fine no materialdeparture from the salient feasets of numbers I5, I6 which occur inincreastures of the invention. ing values toward-theindex line II wherethey The so-called triangle I is intended to be made stop. y t f 40 outof a sheetof Celluloid of a suitable thickness, The scale I2 is ya.scale-of linear ratios or values or any other suitable substitute. Inits general and its markings end at one side of a slot I'I n aspect thedevice is a triangle, but inasmuch which extends in 'parallelism `to thebase line 5. as the profile of the side 2 is cut on a curve the Thisslot has slightly enlarged terminals I8, the ""45winstrument is not atrue triangle, but is substanleft hand one of *which occurs directly ona line 45 tially so, and for convenience in reference is t I9 inscribedin the face of the triangle and herein called a triangle. The triangleincludes marked 30 line, rinasmuch as this line stands at the baseportion 3 and the hypotenusevll. Base a 30. inclination to the base line5. The line I9 -and hypotenuse lines 5, 6 are inscribed inthe has itsorigin at the vertex 'I of the angle defined 4-5ojsurface of thetriangle at a slight distance in by the lines 5, 6 and II. The purposeof the slot 50 from and parallel to the respective base portion I'I isto enable the insertion offa pencil point so 3, and hypotenuse 4. Theselines and all other that armark can be made on the paper oppositeinscriptions on the face of the triangle areprefto the desired'ne of thedivisions of the scale I2. erably4 lilled with a colored pigment so asto be It is to be observed that the scale I3 is carried easilydiscernible. out only in part at the opposite extremities of the 55 baseof the triangle. The obvious purpose here is to avoid running the scalemarkings up into the lines 6, I9 at the left and into the markings ofthe scale I4 at the right. Thus it will be understood that I2 and I3 areone and the same scale, the graduations at the left and rightextremities simply branching 01T on opposite sides of the base line 5 toavoid confusion.

The scale I4 in the same division still under discussion is a uniformscale, graduated from to 45 (a little over the 45 being shown). Thisscale is used in plotting on a map the results of certain surveyingoperations. Before proceeding with the scales in the Isecond divisionattention is directed to the structure of the slot II. In order torender the graduations I2 more definitely visible, one edge of the slotis Abeveled at 20 (Fig. 3). This bevel prevents the possibility of ashadow falling on the graduations I2 and thereby insures the visibilityof the graduations. As a ymatterrof convenience the graduations I2 andslot Il are supplemented with the designation lines as at 2| so astoenable the user to distinguish from the second division of scalesdesignated circles, as at 22.

T his second division of scales consists of inscribed lines 23, 24,25,*upon which holes 26, 2'I, 28 are drilled through the triangle andtapered (Fig. 2). The series of holes along the respective lines 23, 24and 25 are variously spaced and the holes are designated with numbers,as shown. A large hole 29 at a convenient place in the triangle aids themanipulation of the latter.

The use of the various scales is best understood from the description ofa rfew examples, it being thought unnecessary to describe more than afew because in actual practice the triangle has many more uses thancould be conveniently set out here. Reference is made to Fig. 4 whichillustrates the problem of dividing a given line into an equal number ofparts, say four equal parts. The given linel 30 is locatedperpendicularly to the base line 5. This is done by resting the baseportion 3 of the triangle I on a T-square and manipulating both untilthe given line 30 becomes parallel to the index line II, whereupon thetriangle I is slid to the right on the edge of the T-square outintoview. Sliding continues until the extremities 3|, 32of the given line 30coincide with the base and hypotenuse lines 5, 6.

The pencil point isnow used to make a mark 33 on the paper through thehole "I and a second mark 34 on the paper through that hole in the scaleline 23 designated bythe numeral 4. By now removing the triangle andusing it to guide the pencil point for connecting the marks 33, 34 by aline 35, it will be found that the latter intersects the given line 30at the point 36 which is one-fourth the length of the given line. Theother numerals along the scale line 23 indicate other fractions intovwhich given lines can be divided.

The next example selected is that of describing a regular polygon withinthe given circle 37, and reference is made to Fig. for an outline of theoperations. The polygon is intended to have nine sides, but the numbermay be more or less as will be understood from the numeral designationsrunning along the holes in the scale line 24 which is the one now used.The center 38 of the circle is made to coincide with the base line 5,and. the radial line 39 is placed perpendicularly to said base lineaccording to the. method described in connection with Fig. 4.

The triangle I is slid along the edge of the T- square until thecircumferential point 40 touches the 30 line I9. A pencil mark 4I is nowmade on the paper through the hole I and a similar mark 42 is made onthe paper through the hole 9, this designating the number of sides ofthe polygon. A line 43 connecting the marks 4I, 42 if extended farenough beyond the mark 42, Will intersect the circle 3'I at the point 44which will be found to be one-ninth of the circumference. Thismeasurement can be stepped off, as indicated at 45, and whencorresponding measurements are connected by chord lines 46, theresulting gure will be a regular polygon.

A third and last example involves the use of the scale I4 in plotting ona map an observed inclination to the horizon of any given distanceremote from a given stadia or observation station of the surveyor. Thedistance between two stakes or stations, measures `along an inclineddistance, is not given on the final map which Will, therefore, show anapparent horizontal distance instead of the true condition of theterrain.

Suppose that the distance between two rods is 750 yards and that theobserved vertical angle is 30. According to Fig. 6, the triangle isplaced on the map (not shown) in such a manner that the base line 5coincides with the stadia station, and the course line 5I isperpendicular to said base line. This is accomplished by making thecourse line 5I coincide with the index line II and by sliding thetriangle I along the edge of the T- 'square until the course line isperpendicular to the base line and coincides at the point 41 Where thescale I2 indicates a distance corresponding.

to the intercepted space on the stadi-a rod, in this case '750 yards asindicated at 48.

The horizontal distance is then completed by making a pencil mark 49 onthe map through the hole 8, this being the origin of both the right handside 4of scale I2 and of the scale I4. Another pencil mark 50 is made onthe map at the place coinciding with the observed vertical angle, namely30. By connecting the marks 49, 50 with a line 53 which is extended farenough to intersect the course line 5I, the point 52 Where theintersection occurs denotes the proper reduced distance. Said point 52will be the next transit station from which to lay off the succeedingcourse line.

I claim:

l. In an instrument of precision, a triangular body having a base lineand a slot parallel to said base line, said body also having van indexline perpendicular to the base line, a scale along said mon origin, oneline of said pair of lines constituting a base line, a slot in said bodyparallel to said base line, and a scale between the base line and slot,beginning at said point of origin, said slot beginning at a point Wherea perpendicular to said bas line at one of the graduations of said scaleintersects the other line of said pair of lines.

HARMODIO A. DE VALLE ARIZPE.

,55 slot, the spacing of the slot from the base line"

